PS53011C/PS71020E Lab Worksheet

0.1 📊 Lab Instructions

This week’s lab will explore multiple regression using tidyverse principles!

0.2 📽️ Slides

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1 Week 4: Multiple Regression (Part 1)

Please attempt all questions in your own words. Model answers will be available on the VLE page following the lab session.

2 Learning Outcomes

Conduct simple and multiple linear regression analyses using R and the Tidyverse.
Explore relationships between regression coefficients and correlation measures.
Assess assumptions of linear regression including normality, linearity, and multicollinearity.
Compute and interpret simple, partial, and semipartial correlations in R.

3 Materials

Software: R (Tidyverse package)
Dataset:

library(tidyverse)

4 Dataset Overview

The dataset includes reaction time (RT) data for participants responding to emotional facial expressions. Of particular interest is the average RT to fearful faces for correct identifications. Predictors include:

traitanx: Trait anxiety (Spielberger scale)
ACS: Attentional Control Scale score
Age: Participant age

5 Task 1: Descriptive Statistics and Visualisation

Load the dataset
Create summary statistics and visualizations for RT, traitanx, ACS, and Age.

fearful_data <- read_csv("data/fearful_faces.csv")

fearful_data %>%
  summarise(across(c(Fearful_face_RT, Happy_face_RT, traitanx, ACS, Age), list(mean = mean, sd = sd), na.rm = TRUE))

Fearful_face_RT_mean	Fearful_face_RT_sd	Happy_face_RT_mean	Happy_face_RT_sd	traitanx_mean	traitanx_sd	ACS_mean	ACS_sd	Age_mean	Age_sd
0.4913926	0.0603538	0.4889262	0.0599826	41.67532	10.24238	50.19737	8.294608	23.38462	7.047576

fearful_data %>%
  pivot_longer(cols = c(Fearful_face_RT, Happy_face_RT, traitanx, ACS, Age), names_to = "variable", values_to = "value") %>%
  ggplot(aes(x = value)) +
  geom_histogram(bins = 30, fill = "steelblue", color = "white") +
  facet_wrap(~ variable, scales = "free") +
  theme_minimal()

6 Task 2: Correlation Analysis

Compute a correlation matrix
Visualize relationships using scatterplots

fearful_data %>%
  select(Fearful_face_RT, Happy_face_RT, traitanx, ACS, Age) %>%
  cor(use = "complete.obs") %>%
  round(2)

                Fearful_face_RT Happy_face_RT traitanx   ACS   Age
Fearful_face_RT            1.00          0.96    -0.33  0.18  0.04
Happy_face_RT              0.96          1.00    -0.37  0.14  0.02
traitanx                  -0.33         -0.37     1.00 -0.36 -0.14
ACS                        0.18          0.14    -0.36  1.00  0.36
Age                        0.04          0.02    -0.14  0.36  1.00

pairs(fearful_data %>% select(Fearful_face_RT, Happy_face_RT, traitanx, ACS, Age), main = "Scatterplot Matrix")

7 Task 3: Multiple Regression

Conduct a multiple regression predicting Fearful_face_RT from traitanx, ACS, and Age.

model <- lm(Fearful_face_RT ~ traitanx + ACS + Age, data = fearful_data)
summary(model)


Call:
lm(formula = Fearful_face_RT ~ traitanx + ACS + Age, data = fearful_data)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.105742 -0.043660 -0.002261  0.044587  0.116670 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.5470081  0.0637205   8.584  1.9e-12 ***
traitanx    -0.0018929  0.0007492  -2.527   0.0138 *  
ACS          0.0005506  0.0009446   0.583   0.5619    
Age         -0.0002299  0.0010605  -0.217   0.8290    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.05698 on 68 degrees of freedom
  (17931 observations deleted due to missingness)
Multiple R-squared:  0.1149,    Adjusted R-squared:  0.07587 
F-statistic: 2.943 on 3 and 68 DF,  p-value: 0.0391

8 Task 4: Model Diagnostics

Check linear regression assumptions.

par(mfrow = c(2, 2))
plot(model)

9 Task 5: Partial and Semipartial Correlations

# Load required libraries
library(tidyverse)
library(ppcor)


# Calculate partial correlations
partial_data <- fearful_data %>%
  dplyr::select(Fearful_face_RT, traitanx, ACS, Age) %>%
  drop_na()
pcor_result <- pcor(partial_data, method = "pearson")
pcor_result

$estimate
                Fearful_face_RT    traitanx         ACS         Age
Fearful_face_RT      1.00000000 -0.29295465  0.07051172 -0.02627832
traitanx            -0.29295465  1.00000000 -0.29776049 -0.02300362
ACS                  0.07051172 -0.29776049  1.00000000  0.33458467
Age                 -0.02627832 -0.02300362  0.33458467  1.00000000

$p.value
                Fearful_face_RT   traitanx         ACS         Age
Fearful_face_RT      0.00000000 0.01384887 0.561885102 0.829035513
traitanx             0.01384887 0.00000000 0.012298804 0.850075844
ACS                  0.56188510 0.01229880 0.000000000 0.004640019
Age                  0.82903551 0.85007584 0.004640019 0.000000000

$statistic
                Fearful_face_RT   traitanx        ACS        Age
Fearful_face_RT       0.0000000 -2.5266180  0.5829054 -0.2167714
traitanx             -2.5266180  0.0000000 -2.5720632 -0.1897429
ACS                   0.5829054 -2.5720632  0.0000000  2.9277975
Age                  -0.2167714 -0.1897429  2.9277975  0.0000000

$n
[1] 72

$gp
[1] 2

$method
[1] "pearson"

10 Task 6: Semipartial (Part) Correlation

This task explores how to isolate the unique contribution of one predictor (e.g., trait anxiety) to a dependent variable (reaction time), controlling for other variables only in the predictor.

10.1 Objective

Calculate a semipartial correlation between Fearful_face_RT and traitanx, controlling for ACS and Age only in the predictor.

# Load tidyverse if not already
library(tidyverse)

# Ensure your data is clean
semipartial_data <- fearful_data %>%
  dplyr::select(Fearful_face_RT, traitanx, ACS, Age) %>%
  drop_na()

# Step 1: Residualize the predictor (traitanx ~ ACS + Age)
resid_traitanx <- lm(traitanx ~ ACS + Age, data = semipartial_data)$residuals

# Step 2: Compute correlation between raw DV and residualized predictor
semipartial_corr <- cor(semipartial_data$Fearful_face_RT, resid_traitanx)
semipartial_corr

[1] -0.2882545

Note

Interpretation: This semipartial correlation represents the unique association between trait anxiety and fearful face reaction time, controlling for ACS and Age only in trait anxiety. Unlike partial correlation, it leaves the DV unadjusted.

11 Reflection

How does anxiety influence reaction time to fearful faces?
Does attentional control modify this relationship?
Are the findings specific to fearful stimuli, or would they generalize to other emotional expressions?

Review your code and interpretations. Cross-reference with theoretical models on anxiety and attentional control.

--- title: PS53011C/PS71020E Lab Worksheet format: html: code-tools: true code-overflow: wrap code-annotations: hover code-block-bg: true code-block-border-left: true toc: true number-sections: true df-print: kable engine: knitr pdf: code-overflow: wrap execute: echo: true warning: false message: false error: true --- ### 📊 Lab Instructions This week's lab will explore multiple regression using tidyverse principles! --- ::: {.content-visible when-format="html"} ### 📽️ Slides <div style="position: relative; padding-top: 56.25%; height: 0; overflow: hidden;"> <iframe src="placeholders/lab_slides.html" style="position: absolute; top: 0; left: 0; width: 100%; height: 100%; border: none;" allowfullscreen loading="lazy"> </iframe> </div> > 🧭 **These are your slides for the week!** > > Use the arrow keys to navigate through the slides: > > - ⬅️ and ➡️ to move left and right > - ⬆️ and ⬇️ for nested (vertical) slides > - Press `Esc` to view the **slide overview** > - Press `F` for **fullscreen** (or use browser controls) > - Press `O` to toggle the **overview mode** > - Press `S` to open the **Speaker Notes** window (in presenter mode) > > 💡 Slides are best viewed in **fullscreen** for clarity. ::: ## Week 4: Multiple Regression (Part 1) > Please attempt all questions in your own words. Model answers will be available on the VLE page following the lab session. --- ::: {.learning-outcomes #sec-lab01-LO} ## Learning Outcomes 1. Conduct simple and multiple linear regression analyses using R and the Tidyverse. 2. Explore relationships between regression coefficients and correlation measures. 3. Assess assumptions of linear regression including normality, linearity, and multicollinearity. 4. Compute and interpret simple, partial, and semipartial correlations in R. ::: --- ## Materials ```{r} #| echo: false library(downloadthis) ``` - **Software**: R (Tidyverse package) - **Dataset**: {{< downloadthis data/fearful_faces.csv dname=fearful_faces label="Download the fearful_faces data" icon=database-fill-down type=info class=data-button id=fearful_faces >}} ```{r} #| label: load-libraries #| message: false #| warning: false library(tidyverse) ``` --- ## Dataset Overview The dataset includes reaction time (RT) data for participants responding to emotional facial expressions. Of particular interest is the average RT to fearful faces for correct identifications. Predictors include: - `traitanx`: Trait anxiety (Spielberger scale) - `ACS`: Attentional Control Scale score - `Age`: Participant age --- ## Task 1: Descriptive Statistics and Visualisation - Load the dataset - Create summary statistics and visualizations for RT, traitanx, ACS, and Age. ```{r} #| label: descriptives fearful_data <- read_csv("data/fearful_faces.csv") fearful_data %>% summarise(across(c(Fearful_face_RT, Happy_face_RT, traitanx, ACS, Age), list(mean = mean, sd = sd), na.rm = TRUE)) fearful_data %>% pivot_longer(cols = c(Fearful_face_RT, Happy_face_RT, traitanx, ACS, Age), names_to = "variable", values_to = "value") %>% ggplot(aes(x = value)) + geom_histogram(bins = 30, fill = "steelblue", color = "white") + facet_wrap(~ variable, scales = "free") + theme_minimal() ``` --- ## Task 2: Correlation Analysis - Compute a correlation matrix - Visualize relationships using scatterplots ```{r} #| label: correlations fearful_data %>% select(Fearful_face_RT, Happy_face_RT, traitanx, ACS, Age) %>% cor(use = "complete.obs") %>% round(2) pairs(fearful_data %>% select(Fearful_face_RT, Happy_face_RT, traitanx, ACS, Age), main = "Scatterplot Matrix") ``` --- ## Task 3: Multiple Regression - Conduct a multiple regression predicting Fearful_face_RT from traitanx, ACS, and Age. ```{r} #| label: regression-model model <- lm(Fearful_face_RT ~ traitanx + ACS + Age, data = fearful_data) summary(model) ``` --- ## Task 4: Model Diagnostics - Check linear regression assumptions. ```{r} #| label: diagnostics par(mfrow = c(2, 2)) plot(model) ``` --- ## Task 5: Partial and Semipartial Correlations ```{r} #| label: part-corr #| #| message: false #| warning: false # Load required libraries library(tidyverse) library(ppcor) # Calculate partial correlations partial_data <- fearful_data %>% dplyr::select(Fearful_face_RT, traitanx, ACS, Age) %>% drop_na() pcor_result <- pcor(partial_data, method = "pearson") pcor_result ``` --- ## Task 6: Semipartial (Part) Correlation > This task explores how to isolate the unique contribution of one predictor (e.g., trait anxiety) to a dependent variable (reaction time), controlling for other variables only in the predictor. ### Objective - Calculate a semipartial correlation between `Fearful_face_RT` and `traitanx`, controlling for `ACS` and `Age` **only in the predictor**. ```{r} #| label: semipartial-correlation #| message: false #| warning: false # Load tidyverse if not already library(tidyverse) # Ensure your data is clean semipartial_data <- fearful_data %>% dplyr::select(Fearful_face_RT, traitanx, ACS, Age) %>% drop_na() # Step 1: Residualize the predictor (traitanx ~ ACS + Age) resid_traitanx <- lm(traitanx ~ ACS + Age, data = semipartial_data)$residuals # Step 2: Compute correlation between raw DV and residualized predictor semipartial_corr <- cor(semipartial_data$Fearful_face_RT, resid_traitanx) semipartial_corr ``` ::: {.callout-note} **Interpretation:** This semipartial correlation represents the unique association between trait anxiety and fearful face reaction time, controlling for ACS and Age **only in trait anxiety**. Unlike partial correlation, it leaves the DV unadjusted. ::: --- ## Reflection - How does anxiety influence reaction time to fearful faces? - Does attentional control modify this relationship? - Are the findings specific to fearful stimuli, or would they generalize to other emotional expressions? > Review your code and interpretations. Cross-reference with theoretical models on anxiety and attentional control.